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Shor's algorithm with fewer (pure) qubits
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In this note we consider optimised circuits for implementing Shor's quantum factoring algorithm. First I give a circuit for which none of the about 2n qubits need to be initialised (though we still have to make the usual 2n measurements later on). Then I show how the modular additions in the algorithm can be carried out with a superposition of an arithmetic sequence. This makes parallelisation of Shor's algorithm easier. Finally I show how one can factor with only about 1.5n qubits, and maybe even fewer.
Forward citations
Cited by 2 Pith papers
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Quantum Uncomputation of Clean and Dirty Ancilla Qubits
Quantum compilers can now automatically uncompute dirty ancillas with a rewrite-based normalizer, and the existence problem is coNP-hard.
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Parallel Spooky Pebbling Makes Regev Factoring More Practical
Parallel spooky pebbling reduces Regev factoring multiplication depth to 193 for 4096-bit N, beating prior Regev variants while remaining space-heavier than Shor.
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